1. Michael Cohen, President Trump’s former lawyer, was sentenced to three years in prison, in part for his role in a scheme during the 2016 campaign to buy the silence of two women who said they had affairs with Mr. Trump.

In federal court in Manhattan, the judge said Mr. Cohen, above, had committed a “veritable smorgasbord” of crimes involving deception and “motivated by personal greed and ambition,” each of which “standing alone warrant serious punishment.”

Mr. Cohen’s sentencing involved a guilty plea in a second case as well, filed by the special counsel, Robert Mueller. Mr. Cohen admitted that he lied to Congress, failing to divulge the extent of Mr. Trump’s involvement in negotiations during the campaign to build a Trump Tower in Moscow.

“I blame myself for the conduct which has brought me here today,” Mr. Cohen told the court, “and it was my own weakness and a blind loyalty to this man that led me to choose a path of darkness over light.”

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CreditDaniel Leal-Olivas/Agence France-Presse — Getty Images

2. Theresa May, Britain’s prime minister, survived a no-confidence vote against her leadership, called by lawmakers in her party who are angry at how she has handled the country’s troubled departure from the European Union.

Mrs. May, above, won the support of 200 Conservative lawmakers, while 117 voted against her, a close margin. The sizable opposition could further imperil her Brexit efforts, experts said.

After the vote, Mrs. May spoke of her “renewed mission”: “delivering the Brexit that people voted for, bringing the country back together and building a country that truly works for everyone.”

Separately, a shooting at a market in Strasbourg, France, was an act of terrorism, officials said. The police were conducting an intensive search for the gunman, who killed at least two people and wounded 12 others.

The move is a clear effort to soothe Democrats eager for a new generation of leadership. Ms. Pelosi, 78, center, won an internal party vote this month to be nominated as speaker, a post she held from 2007 to 2011. But a small group of defectors has been threatening to withhold their support when the new Congress convenes next month.

China has begun to make good on some concessions, but the Trump administration is wary — and plans to ratchet up the pressure on Beijing’s trade, cybersecurity and economic policies.

Adding to the urgency of the planned crackdown, U.S. investigators traced the Marriot hack that exposed the data of around 500 million guests back to a Chinese intelligence-gathering effort that also breached health insurers and security clearance databases.

But President Trump complicated the narrative, saying he’d be willing to intervene in the U.S. case against Meng Wanzhou — the Huawei executive arrested in Canada on accusations that she violated sanctions against Iran — if that would help close a trade deal with China. Ms. Meng, above, has been released on bail awaiting extradition to the U.S. Compounding tensions, Beijing has said that a Canadian former diplomat detained in China worked for an organization that was not legally registered, but didn’t divulge any specific accusations or even officially confirm his arrest. Some experts see the case as retribution for Ms. Meng’s arrest. But China has a long history of holding foreigners for undisclosed reasons.

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CreditErin Schaff for The New York Times

5. Rudy Giuliani, President Trump’s personal lawyer, traveled this week to Bahrain, a U.S. ally in the Middle East — but not on official business. He was there hoping to land a consulting contract with the government, which has a record of human rights abuses.

He’s not a government employee and is not subject to government ethics rules. And he has said his efforts are unrelated to — and don’t capitalize on — his representation of the president.

But Mr. Giuliani’s various interests can lead to confusion over the nature of his role. And foreign officials who have reason to want to get in or stay in the Trump administration’s good graces could view hiring Mr. Giuliani’s firm as a good way of doing so, according to ethics watchdogs.

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CreditEric Risberg/Associated Press

6. An artists’ utopia known as the Ghost Ship became the site of one of the nation’s deadliest structural fires in December 2016.

Most of the 36 people who died were attending a party on the second floor of the converted warehouse in Oakland, Calif., above, and were unable to escape down a makeshift staircase.

Max Harris lived at the Ghost Ship, in exchange for chores and collecting the rent. Now he is in jail, facing trial for the deaths — including some of his close friends. He studies Zen Buddhism, keeps the Jewish Sabbath and prays to his Christian God, our writer found, with the hope that something positive might come of the families’ grief.

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7. “The default is never ‘you are the physician.’”

Doctors, lawyers and other professionals who are people of color told us about the steps they take to bolster their credibility — because they supposedly do not, as one physician says she was told, “look the part.”

Some professionals, above, told us they speak in low tones, hoping to be less intimidating. Others wear their work IDs front and center. A lawyer in South Carolina said he avoided informal clothing on his firm’s casual Fridays.

“At times I have had to show my license to my own clients before they believed that I was the attorney working on their case,” he said.

In a story line that begins this week, a Muppet character whose family faced hunger in past episodes has lost her home. Lily’s family shuttles between shelters, stays with relatives and is taken in by a community center.